# Graph 3x-2y=3 3x-2y=3
Solve for y.
Subtract 3x from both sides of the equation.
-2y=3-3x
Divide each term by -2 and simplify.
Divide each term in -2y=3-3x by -2.
-2y-2=3-2+-3x-2
Cancel the common factor of -2.
Cancel the common factor.
-2y-2=3-2+-3x-2
Divide y by 1.
y=3-2+-3x-2
y=3-2+-3x-2
Simplify each term.
Move the negative in front of the fraction.
y=-32+-3x-2
Dividing two negative values results in a positive value.
y=-32+3×2
y=-32+3×2
y=-32+3×2
y=-32+3×2
Rewrite in slope-intercept form.
The slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.
y=mx+b
Reorder -32 and 3×2.
y=3×2-32
Rewrite in slope-intercept form.
y=32x-32
y=32x-32
Use the slope-intercept form to find the slope and y-intercept.
Find the values of m and b using the form y=mx+b.
m=32
b=-32
The slope of the line is the value of m, and the y-intercept is the value of b.
Slope: 32
y-intercept: -32
Slope: 32
y-intercept: -32
Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values.
Choose 1 to substitute in for x to find the ordered pair.
Replace the variable x with 1 in the expression.
f(1)=3(1)2-32
Simplify the result.
Reorder terms.
f(1)=1⋅32-32
Combine the numerators over the common denominator.
f(1)=1⋅3-32
Simplify the numerator.
Multiply 1 by 3.
f(1)=3-32
Subtract 3 from 3.
f(1)=02
f(1)=02
Divide 0 by 2.
f(1)=0
0
0
The y value at x=1 is 0.
y=0
y=0
Choose 3 to substitute in for x to find the ordered pair.
Replace the variable x with 3 in the expression.
f(3)=3(3)2-32
Simplify the result.
Combine the numerators over the common denominator.
f(3)=3(3)-32
Simplify the numerator.
Multiply 3 by 3.
f(3)=9-32
Subtract 3 from 9.
f(3)=62
f(3)=62
Divide 6 by 2.
f(3)=3
3
3
The y value at x=3 is 3.
y=3
y=3
Create a table of the x and y values.
xy1033
xy1033
Graph the line using the slope and the y-intercept, or the points.
Slope: 32
y-intercept: -32
xy1033
Graph 3x-2y=3     